Can you resolve this equation : (2x-5)/(x-1)=(x-1)/(x+1) ?

Question

Can you resolve this equation : (2x-5)/(x-1)=(x-1)/(x+1) ?

Answer 1

(2x-5)/(x-1)=(x-1)/(x+1)

Answer 2

(2x-5)/(x-1)=(x-1)/(x+1)

cross multiply

2x^2 - 3x - 5 = x^2 - 2x + 1

x^2 - x - 6 = 0

(x - 3) (x + 2) = 0

therefore,

x = 3; x = -2

Answer 3

(2x-5)/(x-1)=(x-1)/(x+1)

=> (2x-5)*(x+1) = (x-1)^2

=> 2x^2 - 3x - 5 = x^2 - 2x + 1

=> x^2 - x - 6 =0

=> x^2 -3x + 2x - 6 =0

=> x(x-3) + 2(x-3) = 0

=> (x-3)*(x+2) =0

Either x = 3 or x = -2

Answer 4

Cross multiply, collect like terms and solve:

(2x - 5)(x + 1) = (x - 1)(x - 1)

2x^2 -3x - 5 = x^2 - 2x + 1

x^2 - x - 6 = 0

(x + 2)(x - 3) = 0

x = -2 or x = 3

Answer 5

(2X-5)/(X-1)=(X-1)/(X+1)

(X+1)(2X-5)=(X-1)(X-1)

2X^2 - 3X -5 = X^2 -2X +1

X^2 - X - 6 = 0

(X-3)(X+2) = 0

X= 3 OR -2

Answer 6

what you have to do is first multiply both sides by (x-1) to get rid of the denominator on the right, so you get:

(2x-5)=((x-1)((x-1))/(x+1)

next you want to get rid of the denominator on the left, so you multiply both sides by (x+1) which is:

(2x-5)(x+1)=(x-1)(x-1)

next just distribute everything:

2x^2-3x-5=x^2-2x+1

and now combine like terms:

x^2-x-6=0

now, factor:

(x-3)(x+2)

and your answer is:

x=3 or -2

Answer 7

first, multiply through the denominators to obtain:

(2x-5)(x+1)=(x-1)(x-1)

multiply each side:

2x^2-3x-5=x^2-2x+1

collect terms:

x^2-x-6=0

(x-3)(x+2)=0

x=3, x=-2

Answer 8

(2x - 5) (x + 1) = (x - 1)(x - 1)

2x² - 3x - 5 = x² - 2x + 1

x² - x - 6 = 0

(x - 3)(x + 2) = 0

x = 3 , x = - 2

Answer 9

(2x - 5)/(x - 1) = (x - 1)/(x + 1)

(2x - 5)(x + 1)/(x - 1) = x - 1

(2x - 5)(x + 1) = (x - 1)(x - 1)

2x*x - 5*x + 2x*1 - 5*1 = x*x - 1*x - x*1 + 1*1

2x^2 - 5x + 2x - 5 = x^2 - x - x + 1

2x^2 - 3x - 5 = x^2 - 2x + 1

2x^2 - x^2 - 3x + 2x - 5 - 1 = 0

x^2 - x - 6 = 0

x^2 + 2x - 3x - 6 = 0

(x^2 + 2x) - (3x + 6) = 0

x(x + 2) - 3(x + 2) = 0

(x + 2)(x - 3) = 0

x + 2 = 0

x = -2

x - 3 = 0

x = 3

∴ x = -2 , 3

Answer 10

(2x-5)÷(x-1) = (x-1)÷(x+1)

Multiply both sides by x-1:

2x-5 = (x-1)²÷(x+1)

Multiply both sides by x+1:

(2x-5)(x+1) = (x-1)²

Multiply out both sides.

Simplify.

Use quadratics to finish.